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Cell[CellGroupData[{
Cell["Bond Graphs", "Title"],

Cell["Click the blue arrows on the right to expand the sections.", "SmallText"],

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The notation is not necessary for package operation. It just makes the \
examples in this notebook look nice.\
\>", "SmallText"],

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Cell["\<\
This package can't handle transformers, gyrators, multidimensional bonds, or \
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hard to add though.\
\>", "Text"]
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Cell[BoxData[
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Cell[BoxData[
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            "0", "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", "\<\" \"\
\>", "\<\" \"\>"},
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            "0", "\<\" \"\>", "\<\"\[RightVector]\"\>", "\<\" \"\>", "\<\"\
\[RightVector]\"\>", "\<\" \"\>"},
          {\(0\_f\), "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", 
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\>", "\<\" \"\>"},
          {\(C\_e\), "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", \
"\<\" \"\>", "0", "\<\" \"\>", "\<\" \"\>", "\<\" \"\>"},
          {\(R\_g\), "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", \
"\<\" \"\>", "\<\" \"\>", "0", "\<\" \"\>", "\<\" \"\>"},
          {\(1\_h\), "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", \
"\<\" \"\>", "\<\" \"\>", "\<\" \"\>", "0", "\<\" \"\>"},
          {\(SF\_i\), "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", "\<\" \"\>", "\<\
\" \"\>", "\<\" \"\>", "\<\" \"\>", "\<\"\[RightVector]\"\>", "0"}
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        RowSpacings->1,
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          C[ e], 
          R[ g], 
          1[ h], 
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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        0\_d \[RightTeeVector] \((\(C\_e\) : 1\/1000)\), 
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        0\_d\[RightVectorBar]1\_h, 
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
    \("BondGraphPlot[bgraph] draws a bond graph with appropriate bonds \
depending on the causality of the graph. This function uses GraphPlot and \
GraphCoordinates from the DiscreteMath`GraphPlot package. You can set the \
Method option for GraphCoordinates in the options for this function. See the \
advanced documentation for GraphPlot online at \
http://documents.wolfram.com/mathematica/functions/\
AdvancedDocumentationGraphPlot for more information on the Method option. \
Other options include BondLengthRatio, FeatureLengthRatio and ImageSize."\)], \
"Print",
  CellTags->"Info3353909331-5146246"]
}, Open  ]],

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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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        RowSpacings->1,
        ColumnSpacings->1,
        RowAlignments->Baseline,
        ColumnAlignments->{Left}],
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          C[ e], 
          R[ g], 
          1[ h], 
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          0[ f], 
          C[ e], 
          R[ g], 
          1[ h], 
          SF[ i]}}, TableSpacing -> {1, 1}]]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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              time] \[Equal] \[DoubleStruckE]\_\(f, h\)[time]\), 
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          "&&", \(\[Gamma]\ \[DoubleStruckF]\_\(f, g\)[
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          "&&", \(\[DoubleStruckE]\_\(d, h\)[
                time] + \[DoubleStruckE]\_\(f, h\)[
                time] + \[DoubleStruckE]\_\(i, h\)[time] \[Equal] 0\), 
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\[DoubleStruckF]\_\(d, h\), \[DoubleStruckF]\_\(f, g\), \
\[DoubleStruckF]\_\(f, h\), \[DoubleStruckF]\_\(i, h\), \
\[DoubleStruckCapitalP]\_\(b, c\)}\)}], "}"}]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Mistroke
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Cell[CellGroupData[{

Cell["Regular Example 3-3 from GNVNOTED", "Subsection"],

Cell[BoxData[
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            1[e] \[RightVector] \[ScriptCapitalI][f, W[1]/gr], 
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            0[h] \[RightVector] C[i, 1/K[2]], 0[h] \[RightVector] 1[j], 
            1[j] \[RightVector] \[ScriptCapitalI][k, W[2]/gr], 
            SE[l, \(-W[2]\)] \[RightVector] 1[j], 1[j] \[RightVector] 0[m], 
            0[m] \[RightVector] C[n, 1/K[3]], 0[m] \[RightVector] 1[o], 
            1[o] \[RightVector] \[ScriptCapitalI][p, W[3]/gr], 
            SE[q, \(-W[3]\)] \[RightVector] 1[o], 1[o] \[RightVector] 0[r], 
            0[r] \[RightVector] C[s, 1/K[4]], 0[r] \[RightVector] 1[t], 
            1[t] \[RightVector] \[ScriptCapitalI][u, W[4]/gr], 
            SE[v, \(-W[4]\)] \[RightVector] 1[t], 1[t] \[RightVector] 0[w], 
            0[w] \[RightVector] C[x, 1/K[5]], 0[w] \[RightVector] 1[y], 
            1[y] \[RightVector] \[ScriptCapitalI][z, W[5]/gr], 
            SE[aa, \(-W[5]\)] \[RightVector] 1[y], 1[y] \[RightVector] 0[bb], 
            1[y] \[RightVector] 0[cc], 0[bb] \[RightVector] C[dd, 1/K[6]], 
            0[cc] \[RightVector] R[ee, \[Gamma]], 0[bb] \[RightVector] 1[ff], 
            0[cc] \[RightVector] 1[ff], 
            1[ff] \[RightVector] SF[gg, 0]}];\)\)], "Input"],

Cell[CellGroupData[{

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Cell[BoxData[
    \({\(SF\_a\) : 0, 1\_b, 0\_c, \(C\_d\) : 9\/5300, 
      1\_e, \(I\_f\) : 50\/gr, \(SE\_g\) : \(-50\), 0\_h, \(C\_i\) : 9\/4700, 
      1\_j, \(I\_k\) : 100\/gr, \(SE\_l\) : \(-100\), 
      0\_m, \(C\_n\) : 9\/7700, 
      1\_o, \(I\_p\) : 150\/gr, \(SE\_q\) : \(-150\), 
      0\_r, \(C\_s\) : 9\/14300, 
      1\_t, \(I\_u\) : 200\/gr, \(SE\_v\) : \(-200\), 
      0\_w, \(C\_x\) : 9\/24500, 
      1\_y, \(I\_z\) : 250\/gr, \(SE\_aa\) : \(-250\), 0\_bb, 
      0\_cc, \(C\_dd\) : 9\/38300, \(R\_ee\) : \[Gamma], 
      1\_ff, \(SF\_gg\) : 0}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
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      Short]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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        1\_e \[RightTeeVector] 0\_h, 
        0\_h \[RightTeeVector] \((\(C\_i\) : 9\/4700)\), 
        0\_h\[RightVectorBar]1\_j, 
        1\_j\[RightVectorBar]\((\(I\_k\) : 
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        1\_j \[RightTeeVector] 0\_m, 
        0\_m \[RightTeeVector] \((\(C\_n\) : 9\/7700)\), 
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        1\_o\[RightVectorBar]\((\(I\_p\) : 
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        1\_t\[RightVectorBar]\((\(I\_u\) : 
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Cell[CellGroupData[{

Cell[BoxData[
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}, Open  ]],

Cell["After a long time...", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(Rule[#, #[200] /. rgsolns[\([1]\)]] &\) /@ rgstatevars\)], "Input"],

Cell[BoxData[
    \({\[DoubleStruckCapitalX]\_\(bb, dd\) \[Rule] \(-0.14420568928331765`\), \
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        0.16530256018176928`, \[DoubleStruckCapitalX]\_\(m, n\) \[Rule] \
\(-0.015984143312278022`\), \[DoubleStruckCapitalX]\_\(r, s\) \[Rule] \
\(-0.10301244360939052`\), \[DoubleStruckCapitalX]\_\(w, x\) \[Rule] \
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}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Implementation", "Section",
  InitializationCell->True],

Cell[CellGroupData[{

Cell["Package Start", "Subsection",
  InitializationCell->True],

Cell[BoxData[
    \(\(BeginPackage["\<BondGraphs`\>"];\)\)], "Input",
  InitializationCell->True]
}, Closed]],

Cell[CellGroupData[{

Cell["Needed Packages", "Subsection",
  InitializationCell->True],

Cell[BoxData[
    \(Needs["\<DiscreteMath`GraphPlot`\>"]\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \( (*Needs["\<Utilities`FilterOptions`\>"]*) \)], "Input",
  InitializationCell->True]
}, Closed]],

Cell[CellGroupData[{

Cell["Usage Messages", "Subsection",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraph::usage = "\<BondGraph[{SE[a,10]\[RightVector]1[b],1[b]\
\[RightVector]\[ScriptCapitalI][c,10],1[b]\[RightVector]0[d],0[d]\
\[RightVector]C[e,1/1000],0[d]\[RightVector]1[h],SF[i,0]\[RightVector]1[h]}] \
represents a bond graph. The example given is that of a typical \
effort/inertia/compliance/ground system. Additional documentation is \
available in the source code for this package.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(Zero::usage = "\<0[label] is a constant effort junction in a bond \
graph with a label. Note that the package presently does not use Zero, but \
uses 0. I originally wrote the package using 0, but this usage message \
apparently can't be associated with something that isn't a symbol.\>";\)\)], \
"Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(One::usage = "\<1[label] is a constant flow junction in a bond graph \
with a label. Note that the package presently does not use One, but uses 1. I \
originally wrote the package using 1, but this usage message apparently can't \
be associated with something that isn't a symbol.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(C::usage = "\<C[label,value] is a capacitance element in a bond graph \
with a label and a value.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(\[ScriptCapitalI]::usage = "\<\[ScriptCapitalI][label,value] is an \
intertia element in a bond graph with a label and a value.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(R::usage = "\<R[label,value] is a resistance element in a bond graph \
with a label and a value.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(SE::usage = "\<SE[label,value] is an effort source in a bond graph \
with a label and a value.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(SF::usage = "\<SF[label,value] is a flow source in a bond graph with \
a label and a value.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(RightVector::usage = "\<lhs \[RightVector] rhs is a bond from \
junction lhs to junction rhs in a bond graph\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(RightTeeVector::usage = "\<lhs \[RightTeeVector] rhs is a bond from \
junction lhs to junction rhs that indicates flow to rhs is set by lhs and \
effort to lhs is set by rhs\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(RightVectorBar::usage = "\<lhs \[RightVectorBar] rhs is a bond from \
junction lhs to junction rhs that indicates effort to rhs is set by lhs and \
flow to lhs is set by rhs\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(LeftVector::usage = "\<lhs \[LeftVector] rhs is a bond from junction \
rhs to junction lhs in a bond graph. The package does not presently recognize \
this bond for input.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(LeftTeeVector::usage = "\<lhs \[LeftTeeVector] rhs is a bond from \
junction rhs to junction lhs that indicates flow to lhs is set by rhs and \
effort to rhs is set by lhs. The package does not presently recognize this \
bond for input.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(LeftVectorBar::usage = "\<lhs \[LeftVectorBar] rhs is a bond from \
junction rhs to junction lhs that indicates effort to lhs is set by rhs and \
flow to rhs is set by lhs. The package does not presently recognize this bond \
for input.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[{
    \(Off[General::"\<spell1\>"]\), "\[IndentingNewLine]", 
    \(\(BondGraphQ::usage = "\<BondGraphQ[bgraph] yeilds True if bgraph is a \
bond graph and False otherwise.\>";\)\), "\[IndentingNewLine]", 
    \(On[General::"\<spell1\>"]\)}], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraphJunctions::usage = "\<BondGraphJunctions[bgraph] gives a \
list of the junctions and elements in bgraph in the order they \
appear.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraphCausality::usage = "\<BondGraphCausality[bgraph] will return \
a bond graph with as many causal strokes as the algorithm can properly \
add.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraphEquations::usage = "\<BondGraphStateEquations[bgraph,ivar] \
returns a system of differential algebraic equations based on bgraph with \
dependant variables named Effort[i,j][ivar], Flow[i,j][ivar], \
Momentum[i,j][ivar] and Displacement[i,j][ivar], where i and j indicate \
element/junction labels and ivar is the independant variable. The output is a \
literal translation of the bond graph into equations, without any \
assumptions.\>";\)\)], "Input",
  InitializationCell->True],

Cell[CellGroupData[{

Cell[BoxData[
    \(Effort::usage = "\<Effort[j1,j2][ivar] represents effort on the bond \
between the junctions j1 and j2. It is a function of the independant \
variable, ivar.\>"\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \("Effort[j1,j2][ivar] represents effort on the bond between the \
junctions j1 and j2. It is a function of the independant variable, ivar."\)], \
"Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Flow::usage = "\<Flow[j1,j2][ivar] represents flow on the bond between \
the junctions j1 and j2. It is a function of the independant variable, \
ivar.\>"\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \("Flow[j1,j2][ivar] represents flow on the bond between the junctions j1 \
and j2. It is a function of the independant variable, ivar."\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Momentum::usage = "\<Momentum[j1,j2][ivar] represents momentum on the \
bond between the junctions j1 and j2. It is a function of the independant \
variable, ivar.\>"\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \("Momentum[j1,j2][ivar] represents momentum on the bond between the \
junctions j1 and j2. It is a function of the independant variable, ivar."\)], \
"Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Displacement::usage = "\<Displacement[j1,j2][ivar] represents \
displacement on the bond between the junctions j1 and j2. It is a function of \
the independant variable, ivar.\>"\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \("Displacement[j1,j2][ivar] represents displacement on the bond between \
the junctions j1 and j2. It is a function of the independant variable, ivar."\
\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(BondGraphStateEquations::usage = \
"\<BondGraphStateEquations[bondgraph,ivar] returns a system of first order \
linear differential equations based on bgraph with dependant state variables \
named Momentum[i,j][ivar] and/or Displacement[i,j][ivar], where i and j \
indicate element/junction labels and ivar is the independant variable. This \
function drops equations of the Unequal type.\>";\)\)], "Input",
  InitializationCell->True],

Cell[CellGroupData[{

Cell[BoxData[
    \(BondGraphEquationsOutput::usage = "\<BondGraphEquationsOutput is an \
option to save evaluation time for BondGraphStateEquations by feeding it the \
output of BondGraphEquations (with the same arguments)\>"\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \("BondGraphEquationsOutput is an option to save evaluation time for \
BondGraphStateEquations by feeding it the output of BondGraphEquations (with \
the same arguments)"\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(BondGraphMatrix::usage = "\<BondGraphMatrix[bgraph] replaces allowed \
bonds in favor of List while eliminating the outer BondGraph wrapper of \
bgraph\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraphAdjacenceMatrix::usage = "\<BondGraphAdjacenceMatrix[bgraph] \
gives the directed adjacence matrix of the bond graph bgraph, where bonds are \
indicated by the presence of a (type of) RightVector\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraphAdjacenceTable::usage = "\<BondGraphAdjacenceTable[bgraph] \
will pretty print BondGraphAdjacenceMatrix[bgraph]\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraphUndirectedAdjacenceMatrix::usage = \
"\<BondGraphAdjacenceMatrix[bgraph] gives the \"undirected\" adjacence matrix \
of the bond graph bgraph, where bonds are indicated by the presence of a \
(type of) RightVector or LeftVector\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraphUndirectedAdjacenceTable::usage = \
"\<BondGraphUndirectedAdjacenceTable[bgraph] will pretty print \
BondGraphUndirectedAdjacenceMatrix[bgraph]\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraphUndirectedAdjacenceCountMatrix::usage = \
"\<BondGraphAdjacenceCountMatrix[bgraph] gives the \"undirected\" adjacence \
matrix of the bond graph bgraph, where bonds are indicated by the presence of \
a 1\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraphUndirectedAdjacenceCountTable::usage = \
"\<BondGraphUndirectedAdjacenceCountTable[bgraph] will pretty print \
BondGraphUndirectedAdjacenceCountMatrix[bgraph]\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraphPlot::usage = "\<BondGraphPlot[bgraph] draws a bond graph \
with appropriate bonds depending on the causality of the graph. This function \
uses GraphPlot and GraphCoordinates from the DiscreteMath`GraphPlot package. \
You can set the Method option for GraphCoordinates in the options for this \
function. See the advanced documentation for GraphPlot online at \
http://documents.wolfram.com/mathematica/functions/\
AdvancedDocumentationGraphPlot for more information on the Method option. \
Other options include BondLengthRatio, FeatureLengthRatio and \
ImageSize.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondLengthRatio::usage = "\<BondLengthRatio is an option for \
BondGraphPlot that determines the ratio of drawn bond length to junction \
separation distance.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(FeatureLengthRatio::usage = "\<FeatureLengthRatio is an option for \
BondGraphPlot that determines the width of a bond relative to its' drawn \
length.\>";\)\)], "Input",
  InitializationCell->True]
}, Closed]],

Cell[CellGroupData[{

Cell["Private Definitions Start", "Subsection",
  InitializationCell->True],

Cell[BoxData[
    \(\(Begin["\<`Private`\>"];\)\)], "Input",
  InitializationCell->True]
}, Closed]],

Cell[CellGroupData[{

Cell["Allowed Bonds", "Subsection",
  InitializationCell->True],

Cell[BoxData[
    \(\($AllowedBonds = 
        RightVector | RightTeeVector | RightVectorBar;\)\)], "Input",
  InitializationCell->True]
}, Closed]],

Cell[CellGroupData[{

Cell["Pattern Tests", "Subsection",
  InitializationCell->True],

Cell["\<\
BondGraphJunctionQ yields True for a junction and False otherwise.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphJunctionQ[junction_] := 
      MatchQ[junction, \((C | \[ScriptCapitalI] | R | SE | SF)\)[b_, 
            xp_] | \((1 | 0)\)[b_]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphJunctionListQ yields True for a list of junctions and False \
otherwise.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphJunctionListQ[junctions_] := 
      MatchQ[junctions, {__?BondGraphJunctionQ}]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphJunctionListsQ yields True for a list of junction lists and False \
otherwise.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[{
    \(Off[General::"\<spell1\>"]\), "\[IndentingNewLine]", 
    \(BondGraphJunctionListsQ[junctionlists_] := 
      MatchQ[junctionlists, {__?
            BondGraphJunctionListQ}]\), "\[IndentingNewLine]", 
    \(On[General::"\<spell1\>"]\)}], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphBondQ yields True for a bond and False otherwise. It can accept an \
option to allow a more limited set of causal strokes.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[{
    \(Off[General::"\<spell1\>"]\), "\[IndentingNewLine]", 
    \(\(Options[
          BondGraphBondQ] = {AllowedBonds \[Rule] $AllowedBonds};\)\), "\
\[IndentingNewLine]", 
    \(On[General::"\<spell1\>"]\)}], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphBondQ[bond_, opts___] := 
      MatchQ[bond, \((\(AllowedBonds /. {opts}\) /. 
              Options[BondGraphBondQ])\)[_?BondGraphJunctionQ, _?
            BondGraphJunctionQ]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphBondQ yields True for a list of bonds and False otherwise. It can \
accept an option to allow a more limited set of causal strokes.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(\(Options[
          BondGraphBondListQ] = {AllowedBonds \[Rule] $AllowedBonds};\)\)], \
"Input",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphBondListQ[bonds_, opts___] := 
      MatchQ[bonds, {PatternTest[__, 
            BondGraphBondQ[#, 
                AllowedBonds \[Rule] \((\(AllowedBonds /. {opts}\) /. 
                      Options[BondGraphBondListQ])\)] &]}]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphQ yields True for a bond graph and False otherwise. It can accept an \
option to allow a more limited set of causal strokes.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(\(Options[
          BondGraphQ] = {AllowedBonds \[Rule] $AllowedBonds};\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphQ[bg_, opts___] := 
      MatchQ[bg, 
        BondGraph[
          PatternTest[_, 
            BondGraphBondListQ[#, 
                AllowedBonds \[Rule] \((\(AllowedBonds /. {opts}\) /. 
                      Options[BondGraphBondListQ])\)] &]]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphBondContainsJunctionQ yields True for a bond containing a given \
junction and False otherwise. It can accept an option to allow a more limited \
set of causal strokes.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(\(Options[
          BondGraphBondContainsJunctionQ] = {AllowedBonds \[Rule] \
$AllowedBonds};\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphBondContainsJunctionQ[bond_?BondGraphBondQ, 
        junction_?BondGraphJunctionQ, opts___?OptionQ] := 
      And[MemberQ[bond, junction], 
        BondGraphBondQ[bond, 
          AllowedBonds \[Rule] \((\(AllowedBonds /. {opts}\) /. 
                Options[BondGraphBondContainsJunctionQ])\)]]\)], "Input",
  InitializationCell->True]
}, Closed]],

Cell[CellGroupData[{

Cell["Core Functions", "Subsection",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphJunctions[
        bg_?BondGraphQ] := \(Reap[
          Sow[1, Sequence @@@ First[bg]], _, #1 &]\)[\([2]\)]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphMatrix replaces $AllowedBonds in favor of List while eliminating the \
outer BondGraph wrapper.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphMatrix[bg_?BondGraphQ] := 
      List @@ Apply[Sequence, Apply[List, bg, {2}], {1}]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphAdjacenceMatrix gives a directed adjacence matrix, where bonds are \
indicated by the presence of a RightVector.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[{
    \(\(Options[
          BondGraphAdjacenceMatrix] = {JunctionList \[Rule] 
            Automatic};\)\), "\n", 
    \(BondGraphAdjacenceMatrix[bg_?BondGraphQ, opts___] := 
      Module[{junctions = \(JunctionList /. {opts}\) /. 
              Options[BondGraphAdjacenceMatrix], adj}, 
        If[junctions \[Equal] Automatic, junctions = BondGraphJunctions[bg]]; 
        adj = Table[0, {Length[junctions]}, {Length[junctions]}]; 
        Scan[Function[Set[Part[adj, Sequence @@ #], Head@#]], 
          bg[\([1]\)] /. MapIndexed[Rule[#1, First[#2]] &, junctions]]; 
        adj]\)}], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphUndirectedAdjacenceMatrix gives an \"undirected\" adjacence matrix. \
Forward bonds are indicated by the presence of a (type of) RightVector. \
Backward bonds are indicated by the presence of a (type of) LeftVector. The \
diagonal is filled with zeros.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[{
    \(\(Options[
          BondGraphUndirectedAdjacenceMatrix] = {JunctionList \[Rule] 
            Automatic};\)\), "\n", 
    \(BondGraphUndirectedAdjacenceMatrix[bg_?BondGraphQ, opts___?OptionQ] := 
      Module[{junctions = \(JunctionList /. {opts}\) /. 
              Options[BondGraphUndirectedAdjacenceMatrix], adj}, 
        If[junctions \[Equal] Automatic, junctions = BondGraphJunctions[bg]]; 
        adj = Table[0, {Length[junctions]}, {Length[junctions]}]; 
        Scan[Function[Set[Part[adj, Sequence @@ #], Head@#]; 
            Set[Part[adj, Sequence @@ Reverse[#]], 
              Head[#] /. {RightVector \[Rule] LeftVector, 
                  RightTeeVector \[Rule] LeftTeeVector, 
                  RightVectorBar \[Rule] LeftVectorBar}]], 
          bg[\([1]\)] /. MapIndexed[Rule[#1, First[#2]] &, junctions]]; 
        adj]\)}], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphUndirectedAdjacenceCountMatrix gives an undirected adjacence matrix, \
with ones indicating a bond. The matrix is symmetric with zeros on the \
diagonal.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(\(BondGraphUndirectedAdjacenceCountMatrix[bg_?BondGraphQ] := 
        BondGraphUndirectedAdjacenceMatrix[
            bg] /. {RightVector | RightTeeVector | RightVectorBar | 
                LeftVector | LeftTeeVector | LeftVectorBar \[Rule] 
              1};\)\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphJunctionBonds gives a list of all bonds in bg associated with a \
particular junction or element.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphJunctionBonds[bg_?BondGraphQ, junction_?BondGraphJunctionQ] := 
      Module[{x}, 
        Cases[List @@ \(Sequence @@@ bg\), 
          x_ /; BondGraphBondContainsJunctionQ[x, junction]]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphJunctionBonds gives a list of all bonds in bg not associated with a \
particular junction or element.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphNonJunctionBonds[bg_?BondGraphQ, 
        junction_?BondGraphJunctionQ] := 
      Module[{x}, 
        DeleteCases[List @@ \(Sequence @@@ bg\), 
          x_ /; BondGraphBondContainsJunctionQ[x, junction]]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphJunctionPatternCausalityReplacements is a function that returns the \
bond list in its first argument as a bond list having more causal strokes, if \
possible, given the rules of causality assignment as applied to the junction \
under consideration. This function will only properly add causality to the \
bonds if they are from BondGraphJunctionBonds acting on the same \
(aforementioned) junction. The order of rule application is important. A \
different order could result in an invalid causality for the graph. The rule \
order is:

SE (causal stroke is always far)
SF (causal stroke is always close)
1 (strong bond found, assign the rest as weak)
0 (strong bond found, assign the rest as weak)
1 (one bond left, it must be the strong bond)
0 (one bond left, it must be the strong bond)
C (integral causality)
I (integral causality)
R (whatever causality)\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphJunctionPatternCausalityReplacements[
        bonds_?BondGraphBondListQ, junction_?BondGraphJunctionQ] := 
      Module[{x, blah1, blah2, nodepatternreplist}, 
        nodepatternreplist = {{SE[__], 
              RightVector[junction, blah2_] \[RuleDelayed] 
                RightVectorBar[junction, blah2], 
              RightVector[blah1_, junction] \[RuleDelayed] 
                RightTeeVector[blah1, junction]}, {SF[__], 
              RightVector[junction, blah2_] \[RuleDelayed] 
                RightTeeVector[junction, blah2], 
              RightVector[blah1_, junction] \[RuleDelayed] 
                RightVectorBar[blah1, junction]}, {1[_], 
              bondlist_List /; 
                  Or @@ Map[
                      MatchQ[#, 
                          RightTeeVector[_, junction] | 
                            RightVectorBar[junction, _]] &, 
                      bondlist] \[RuleDelayed] 
                ReplaceAll[
                  bondlist, {RightVector[junction, blah2_] \[Rule] 
                      RightTeeVector[junction, blah2], 
                    RightVector[blah1_, junction] \[Rule] 
                      RightVectorBar[blah1, junction]}]}, {0[_], 
              bondlist_List /; 
                  Or @@ Map[
                      MatchQ[#, 
                          RightVectorBar[_, junction] | 
                            RightTeeVector[junction, _]] &, 
                      bondlist] \[RuleDelayed] 
                ReplaceAll[
                  bondlist, {RightVector[junction, blah2_] \[Rule] 
                      RightVectorBar[junction, blah2], 
                    RightVector[blah1_, junction] \[Rule] 
                      RightTeeVector[blah1, junction]}]}, {1[_], 
              bondlist_List /; 
                  Length[Cases[bondlist, 
                        x_ /; BondGraphBondQ[x, 
                            AllowedBonds \[Rule] RightVector]]] \[Equal] 
                    1 \[RuleDelayed] 
                ReplaceAll[
                  bondlist, {RightVector[junction, blah2_] \[Rule] 
                      RightVectorBar[junction, blah2], 
                    RightVector[blah1_, junction] \[Rule] 
                      RightTeeVector[blah1, junction]}]}, {0[_], 
              bondlist_List /; 
                  Length[Cases[bondlist, 
                        x_ /; BondGraphBondQ[x, 
                            AllowedBonds \[Rule] RightVector]]] \[Equal] 
                    1 \[RuleDelayed] 
                ReplaceAll[
                  bondlist, {RightVector[junction, blah2_] \[Rule] 
                      RightTeeVector[junction, blah2], 
                    RightVector[blah1_, junction] \[Rule] 
                      RightVectorBar[blah1, junction]}]}, {C[__], 
              bondlist_List /; Length[bondlist] \[Equal] 1 \[RuleDelayed] 
                ReplaceAll[
                  bondlist, {RightVector[junction, blah2_] \[Rule] 
                      RightVectorBar[junction, blah2], 
                    RightVector[blah1_, junction] \[Rule] 
                      RightTeeVector[blah1, 
                        junction]}]}, {\[ScriptCapitalI][__], 
              bondlist_List /; Length[bondlist] \[Equal] 1 \[RuleDelayed] 
                ReplaceAll[
                  bondlist, {RightVector[junction, blah2_] \[Rule] 
                      RightTeeVector[junction, blah2], 
                    RightVector[blah1_, junction] \[Rule] 
                      RightVectorBar[blah1, junction]}]}, {R[__], 
              bondlist_List /; Length[bondlist] \[Equal] 1 \[RuleDelayed] 
                ReplaceAll[
                  bondlist, {RightVector[junction, blah2_] \[Rule] 
                      RightVectorBar[junction, blah2], 
                    RightVector[blah1_, junction] \[Rule] 
                      RightTeeVector[blah1, junction]}]}}; 
        bonds /. Flatten@
            Cases[nodepatternreplist, 
              x_List /; MatchQ[junction, First[x]] \[RuleDelayed] 
                Sequence @@ Rest[x]]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphCausalityHelperLevelNeg1 feeds \
BondGraphJunctionPatternCausalityReplacements bonds associated with the \
junction under consideration to add causal strokes.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphCausalityHelperLevelNeg1[bg_?BondGraphQ, 
        junction_?BondGraphJunctionQ] := 
      BondGraph[
        Join[BondGraphJunctionPatternCausalityReplacements[
            BondGraphJunctionBonds[bg, junction], junction], 
          BondGraphNonJunctionBonds[bg, junction]]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphCausalityHelperLevelNeg2 iterates BondGraphCausalityHelperLevelNeg1 \
over a list of junctions.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphCausalityHelperLevelNeg2[{bg_, junctions_} /; 
          And[BondGraphQ[bg], BondGraphJunctionListQ[junctions]]] := {Fold[
          BondGraphCausalityHelperLevelNeg1, bg, junctions], 
        junctions}\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphCausalityHelperLevelNeg3 calls BondGraphCausalityHelperLevelNeg2 on \
a list of junctions until the result doesn't change (to make sure causality \
has propagated as far as it can for the present junction list).\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphCausalityHelperLevelNeg3[bg_?BondGraphQ, 
        junctions_?BondGraphJunctionListQ] := 
      First@FixedPoint[
          BondGraphCausalityHelperLevelNeg2, {bg, junctions}]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphCausalityHelperLevelNeg4 iterates BondGraphCausalityHelperLevelNeg3 \
on a list of junction lists, which probably seems dumb until one considers \
that there is a certain order of junction groups that should be iterated over \
to make sure the graph converges to a valid set of causal strokes The order \
of junction groups (aka list of junction lists) is provided by \
BondGraphCausalityJunction lists.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphCausalityHelperLevelNeg4[bg_?BondGraphQ, 
        junctionlists_?BondGraphJunctionListsQ] := 
      Catch[Fold[
          Function[
            If[BondGraphQ[#1, 
                AllowedBonds \[Rule] RightTeeVector | RightVectorBar], 
              Throw[#1], BondGraphCausalityHelperLevelNeg3[##]]], bg, 
          junctionlists]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphCausalityJunctionLists results in a list of junction lists (which \
are of length 1 if they correspond to steps 4 or 6) that, when fed into \
BondGraphCausalityHelperLevelNeg4, propagate causality in the following \
order:
1. From sources (SE or SF element)
2. Through ones and zeros
3. From a second order element (C or I element)
4. Back through ones and zeros
5. Repeating steps 3 and 4 until all second order elements have causal \
strokes and those causal strokes have propagated through the graph
6. From a first order element (R element)
7. Back through ones and zeros
8. Repeating steps 6 and 7 until all first order elements have causal strokes \
and those causal strokes have propagated through the graph\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphCausalityJunctionLists[bg_?BondGraphQ] := 
      Module[{sources, onesnzeros, secondorders, 
          firstorders}, {sources, onesnzeros, secondorders, firstorders} = 
          Map[Cases[BondGraphJunctions[bg], #] &, {SE[__] | SF[__], 
              1[_] | 0[_], C[__] | \[ScriptCapitalI][__], R[__]}]; {sources, 
          onesnzeros, 
          Sequence @@ 
            ReleaseHold[\(Hold[{#}, onesnzeros] &\) /@ secondorders], 
          Sequence @@ 
            ReleaseHold[\(Hold[{#}, onesnzeros] &\) /@ 
                firstorders]}]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphResort is used to make output bond graphs with causality have the \
same bond order as their input bond graphs (without causality). This \
operation only works if the graphs differ only in bond causality type.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphResort[unorderedbg_?BondGraphQ, desiredorderbg_?BondGraphQ] := 
      Module[{repdesiredorderbg = 
            desiredorderbg /. {$AllowedBonds \[Rule] RightVector}}, 
        ReplacePart[desiredorderbg, unorderedbg, 
          Sequence @@ 
            Transpose[\(MapIndexed[{First@
                        Position[repdesiredorderbg, #1], #2} &, 
                  unorderedbg /. {$AllowedBonds \[Rule] 
                        RightVector}, {2}]\)[\([1]\)]]]]\)], "Input",
  InitializationCell->True],

Cell[TextData[{
  "BondGraphCausality will return output the input graph after adding causal \
strokes. By the way, just because a bond graph can have integral causal \
strokes on all bonds does not mean that ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " will be able to solve the resulting equations."
}], "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphCausality[bg_?BondGraphQ] := 
      BondGraphResort[
        BondGraphCausalityHelperLevelNeg4[bg, 
          BondGraphCausalityJunctionLists[bg]], bg]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphJunctionPatternEqualityReplacements is a function that returns the \
bond list in its first argument as a set (sometimes of length one) of \
equations according to the junction and independant variable under \
consideration. Applying a rule only when a corresponding junction type is \
under consideration makes it easier to write each rule. The rules are pretty \
simple, since the code only handles integral causality. Sources of effort set \
effort. Sources of flow set flow. Zero junctions conserve flow and have \
constant effort. One junctions conserve effort and have constant flow. \
Capacitor flow is the derivative of displacement. Capacitor effort is \
displacement divided by capacitance. Inertia effort is the derivative of \
momentum. Inertia flow is momentum divided by inertance. Resistor effort is \
resistance times flow.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphJunctionPatternEqualityReplacements[bonds_?BondGraphBondListQ, 
        junction_?BondGraphJunctionQ, ivar_Symbol] := 
      Module[{x, blah1, blah2, nodepatternreplist}, 
        nodepatternreplist = {{SE[__], 
              RightVectorBar[junction, blah2_] \[RuleDelayed] 
                Equal[junction[\([2]\)], \(Effort[junction[\([1]\)], 
                      blah2[\([1]\)]]\)[ivar]], 
              RightTeeVector[blah1_, junction] \[RuleDelayed] 
                Equal[\(Effort[blah1[\([1]\)], junction[\([1]\)]]\)[ivar], 
                  junction[\([2]\)]]}, {SF[__], 
              RightTeeVector[junction, blah2_] \[RuleDelayed] 
                Equal[junction[\([2]\)], \(Flow[junction[\([1]\)], 
                      blah2[\([1]\)]]\)[ivar]], 
              RightVectorBar[blah1_, junction] \[RuleDelayed] 
                Equal[\(Flow[blah1[\([1]\)], junction[\([1]\)]]\)[ivar], 
                  junction[\([2]\)]]}, {1[_], 
              bondlist_List \[RuleDelayed] {ReplaceAll[
                    Equal[Plus @@ bondlist, 
                      0], {\((RightTeeVector | RightVectorBar)\)[junction, 
                          blah2_] \[RuleDelayed] \(-\(Effort[
                              junction[\([1]\)], blah2[\([1]\)]]\)[
                            ivar]\), \((RightTeeVector | RightVectorBar)\)[
                          blah1_, 
                          junction] \[RuleDelayed] \(Effort[blah1[\([1]\)], 
                            junction[\([1]\)]]\)[ivar]}], 
                  ReplaceAll[
                    Equal @@ bondlist, {\((RightTeeVector | RightVectorBar)\)[
                          junction, 
                          blah2_] \[RuleDelayed] \(Flow[junction[\([1]\)], 
                            blah2[\([1]\)]]\)[
                          ivar], \((RightTeeVector | RightVectorBar)\)[
                          blah1_, 
                          junction] \[RuleDelayed] \(Flow[blah1[\([1]\)], 
                            junction[\([1]\)]]\)[ivar]}]}}, {0[_], 
              bondlist_List \[RuleDelayed] {ReplaceAll[
                    Equal[Plus @@ bondlist, 
                      0], {\((RightTeeVector | RightVectorBar)\)[junction, 
                          blah2_] \[RuleDelayed] \(-\(Flow[junction[\([1]\)], 
                              blah2[\([1]\)]]\)[
                            ivar]\), \((RightTeeVector | RightVectorBar)\)[
                          blah1_, 
                          junction] \[RuleDelayed] \(Flow[blah1[\([1]\)], 
                            junction[\([1]\)]]\)[ivar]}], 
                  ReplaceAll[
                    Equal @@ bondlist, {\((RightTeeVector | RightVectorBar)\)[
                          junction, 
                          blah2_] \[RuleDelayed] \(Effort[junction[\([1]\)], 
                            blah2[\([1]\)]]\)[
                          ivar], \((RightTeeVector | RightVectorBar)\)[
                          blah1_, 
                          junction] \[RuleDelayed] \(Effort[blah1[\([1]\)], 
                            junction[\([1]\)]]\)[ivar]}]}}, {C[__], 
              RightVectorBar[junction, blah2_] \[RuleDelayed] 
                Sequence @@ {Equal[\(Displacement[junction[\([1]\)], 
                            blah2[\([1]\)]]\)[ivar]/
                        junction[\([2]\)], \(Effort[junction[\([1]\)], 
                          blah2[\([1]\)]]\)[
                        ivar]], \(Displacement[junction[\([1]\)], 
                            blah2[\([1]\)]]'\)[
                        ivar] \[Equal] \(Flow[junction[\([1]\)], 
                          blah2[\([1]\)]]\)[ivar]}, 
              RightTeeVector[blah1_, junction] \[RuleDelayed] 
                Sequence @@ {Equal[\(Displacement[blah1[\([1]\)], 
                            junction[\([1]\)]]\)[ivar]/
                        junction[\([2]\)], \(Effort[blah1[\([1]\)], 
                          junction[\([1]\)]]\)[
                        ivar]], \(Displacement[blah1[\([1]\)], 
                            junction[\([1]\)]]'\)[
                        ivar] \[Equal] \(Flow[blah1[\([1]\)], 
                          junction[\([1]\)]]\)[
                        ivar]}}, {\[ScriptCapitalI][__], 
              RightTeeVector[junction, blah2_] \[RuleDelayed] 
                Sequence @@ {Equal[\(Momentum[junction[\([1]\)], 
                            blah2[\([1]\)]]\)[ivar]/
                        junction[\([2]\)], \(Flow[junction[\([1]\)], 
                          blah2[\([1]\)]]\)[
                        ivar]], \(Momentum[junction[\([1]\)], 
                            blah2[\([1]\)]]'\)[
                        ivar] \[Equal] \(Effort[junction[\([1]\)], 
                          blah2[\([1]\)]]\)[ivar]}, 
              RightVectorBar[blah1_, junction] \[RuleDelayed] 
                Sequence @@ {Equal[\(Momentum[blah1[\([1]\)], 
                            junction[\([1]\)]]\)[ivar]/
                        junction[\([2]\)], \(Flow[blah1[\([1]\)], 
                          junction[\([1]\)]]\)[
                        ivar]], \(Momentum[blah1[\([1]\)], 
                            junction[\([1]\)]]'\)[
                        ivar] \[Equal] \(Effort[blah1[\([1]\)], 
                          junction[\([1]\)]]\)[
                        ivar]}}, {R[__], \((RightTeeVector | 
                      RightVectorBar)\)[junction, blah2_] \[RuleDelayed] 
                Equal[\(Effort[junction[\([1]\)], blah2[\([1]\)]]\)[ivar], 
                  Flow[junction[\([1]\)], 
                      blah2[\([1]\)]]*\(junction[\([2]\)]\)[
                      ivar]], \((RightTeeVector | RightVectorBar)\)[blah1_, 
                  junction] \[RuleDelayed] 
                Equal[\(Flow[blah1[\([1]\)], junction[\([1]\)]]\)[ivar]*
                    junction[\([2]\)], \(Effort[blah1[\([1]\)], 
                      junction[\([1]\)]]\)[ivar]]}}; 
        bonds /. Flatten@
            Cases[nodepatternreplist, 
              x_List /; MatchQ[junction, First[x]] \[RuleDelayed] 
                Sequence @@ Rest[x]]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphEquations will return the logical set of equations represented by \
the bond graph and a list of the generated dependant variables. The output \
contains Effort, Flow, Displacement and Momentum variables that have been \
generated from the bonds. If the equations can't be reformatted into Linear \
Time Invariant form after this command returns the equations, I bet that \
DSolve and NDSolve will not like them.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphEquations[
        PatternTest[bg_, 
          BondGraphQ[#, 
              AllowedBonds \[Rule] RightTeeVector | RightVectorBar] &], 
        ivar_Symbol] := 
      Module[{eqns = 
            And @@ Apply[
                And, \(BondGraphJunctionPatternEqualityReplacements[
                      BondGraphJunctionBonds[bg, #], #, ivar] &\) /@ 
                  BondGraphJunctions[bg], {1}]}, {eqns, 
          Cases[Variables[eqns /. Equal | And \[Rule] List], 
            x : \(\((Effort | Flow | Displacement | Momentum)\)[y__]\)[
                  ivar] \[RuleDelayed] Head[x]]}]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphStateEquations will return a system of first order linear \
differential equations and a list of the generated dependant variables based \
on bgraph with dependant indexed state variables named Momentum and \
Dispacement. This function drops equations of the Unequal type.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[{
    \(\(Options[
          BondGraphStateEquations] = {BondGraphEquationsOutput \[Rule] 
            None};\)\), "\[IndentingNewLine]", 
    \(BondGraphStateEquations[
        PatternTest[bg_, 
          BondGraphQ[#, 
              AllowedBonds \[Rule] RightTeeVector | RightVectorBar] &], 
        ivar_Symbol, opts___?OptionQ] := 
      Module[{bgrpheqnsout = 
            If[\((\(BondGraphEquationsOutput /. {opts}\) /. 
                    Options[BondGraphStateEquations])\) === None, 
              BondGraphEquations[bg, 
                ivar], \(BondGraphEquationsOutput /. {opts}\) /. 
                Options[BondGraphStateEquations]], eqns, vars, 
          elimvars}, {eqns, vars} = bgrpheqnsout; 
        elimvars = \(#[ivar] &\) /@ 
            Cases[vars, \((Effort | Flow)\)[__]]; {DeleteCases[
            Eliminate[eqns, elimvars], HoldPattern[Unequal[_, 0]]], 
          Cases[vars, \((Displacement | Momentum)\)[__]]}]\)}], "Input",
  InitializationCell->True]
}, Closed]],

Cell[CellGroupData[{

Cell["Graphics/Pretty Printing", "Subsection",
  InitializationCell->True],

Cell["\<\
BondGraphAdjacenceTable will pretty print BondGraphAdjacenceMatrix\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphAdjacenceTable[bg_?BondGraphQ] := 
      Module[{n, dg}, 
        TableForm[
          BondGraphAdjacenceMatrix[bg] + 
              IdentityMatrix[
                Length[BondGraphJunctions[bg]]] /. {0 -> "\< \>", 
              1 \[Rule] 0, RightVector -> "\<\[RightVector]\>", 
              RightTeeVector \[Rule] "\<\[RightTeeVector]\>", 
              RightVectorBar \[Rule] "\<\[RightVectorBar]\>"}, 
          TableHeadings \[Rule] 
              BondGraphJunctions /@ {bg, bg} /. \(Pattern[n, _]\)[dg__] /; 
                Or[n \[Equal] SE, n \[Equal] C, n \[Equal] SF, 
                  n \[Equal] \[ScriptCapitalI], n \[Equal] R] \[RuleDelayed] 
              n[First@{dg}], TableSpacing \[Rule] {1, 1}]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphUndirectedAdjacenceTable will pretty print \
BondGraphUndirectedAdjacenceMatrix\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphUndirectedAdjacenceTable[bg_?BondGraphQ] := 
      Module[{n, dg}, 
        TableForm[
          BondGraphUndirectedAdjacenceMatrix[bg] + 
              IdentityMatrix[
                Length[BondGraphJunctions[bg]]] /. {0 -> "\< \>", 
              1 \[Rule] 0, RightVector -> "\<\[RightVector]\>", 
              RightTeeVector \[Rule] "\<\[RightTeeVector]\>", 
              RightVectorBar \[Rule] "\<\[RightVectorBar]\>", 
              LeftVector -> "\<\[LeftVector]\>", 
              LeftTeeVector \[Rule] "\<\[LeftTeeVector]\>", 
              LeftVectorBar \[Rule] "\<\[LeftVectorBar]\>"}, 
          TableHeadings \[Rule] 
              BondGraphJunctions /@ {bg, bg} /. \(Pattern[n, _]\)[dg__] /; 
                Or[n \[Equal] SE, n \[Equal] C, n \[Equal] SF, 
                  n \[Equal] \[ScriptCapitalI], n \[Equal] R] \[RuleDelayed] 
              n[First@{dg}], TableSpacing \[Rule] {1, 1}]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphUndirectedAdjacenceCountTable will pretty print \
BondGraphUndirectedAdjacenceCountMatrix\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphUndirectedAdjacenceCountTable[bg_?BondGraphQ] := 
      Module[{n, dg, blah}, 
        TableForm[
          BondGraphUndirectedAdjacenceCountMatrix[bg] + 
              blah\ IdentityMatrix[
                  Length[BondGraphJunctions[bg]]] /. {0 -> "\< \>", 
              blah \[Rule] 0}, 
          TableHeadings \[Rule] 
              BondGraphJunctions /@ {bg, bg} /. \(Pattern[n, _]\)[dg__] /; 
                Or[n \[Equal] SE, n \[Equal] C, n \[Equal] SF, 
                  n \[Equal] \[ScriptCapitalI], n \[Equal] R] \[RuleDelayed] 
              n[First@{dg}], TableSpacing \[Rule] {1, 1}]]\)], "Input",
  InitializationCell->True],

Cell["\<\
UnitVector will create a cartesian vector of magnitude 1 from an input \
cartesian vector.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(\(UnitVector[vec_List] := vec/Norm[vec];\)\)], "Input",
  InitializationCell->True],

Cell["\<\
Perpendicular will create a perpendicular cartesian vector of magnitude 1 \
from an input cartesian vector.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(Perpendicular[s_List, e_List] := 
      UnitVector[
          Most[Cross[Append[e - s, 0], Append[Table[0, {Length[s]}], 1]]]] /; 
        Length[s] \[Equal] Length[e]\)], "Input",
  InitializationCell->True],

Cell["\<\
HalfAboveHalfBelow will create a list of two points when given a center and a \
vector. The displacement between the points is vec. Half the displacement \
between the points yeilds center.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(\(HalfAboveHalfBelow[center_List, vec_List] = {center + vec/2, 
          center - vec/2};\)\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphGraphicsRightTee will give the graphics primitives for a tee given a \
start, end, and feature length (feature length is the width of the bond if \
the distance between start and end is the length of the bond).\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphGraphicsRightTee[s_List, e_List, featlen_?NumericQ] := 
      Line[HalfAboveHalfBelow[s, featlen\ Perpendicular[s, e]]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphGraphicsRightBar will give the graphics primitives for a bar given a \
start, end, and feature length (feature length is the width of the bond if \
the distance between start and end is the length of the bond).\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphGraphicsRightBar[s_List, e_List, featlen_?NumericQ] := 
      Line[HalfAboveHalfBelow[e, featlen\ Perpendicular[s, e]]]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphGraphicsRightVector will draw the graphics primitives for a right \
vector given a start, end, and feature length (feature length is the width of \
the bond if the distance between start and end is the length of the bond).\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphGraphicsRightVector[s_List, e_List, featlen_?NumericQ] := 
      Line[{s, e, 
          e + featlen\ UnitVector[
                s + Norm[e - s]\ Perpendicular[s, e] - e]\ Sqrt[2]/
                2}]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphGraphicsBondStyleFunction will draw the graphics primitives for a \
right vector (with either appropriate causal stroke). It requires the \
adjacence matrix of the bond graph, a fraction for the ratio of drawn bond \
length to junction separation distance, a feature length fraction that \
determines the width of a bond relative to the drawn bond lendth, the \
coordinates of both junctions, and the position of both junctions inside the \
adjacence matrix.\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[
    \(BondGraphGraphicsBondStyleFunction[bgadjmat_?MatrixQ, 
        bondlenfrac_?NumericQ, featlenfrac_?NumericQ, os : {__?NumericQ}, 
        oe : {__?NumericQ}, i_Integer, j_Integer] := 
      Module[{bondlength, bondcenter, s, e, featlen}, 
        bondlength = Norm[oe - os]; 
        bondcenter = Plus[oe, os]/2; {e, s} = 
          HalfAboveHalfBelow[bondcenter, bondlenfrac\ \((oe - os)\)]; 
        featlen = 
          bondlength*bondlenfrac*featlenfrac; {BondGraphGraphicsRightVector[
            s, e, featlen], 
          Which[bgadjmat[\([i, j]\)] === RightTeeVector, 
            BondGraphGraphicsRightTee[s, e, featlen], 
            bgadjmat[\([i, j]\)] === RightVectorBar, 
            BondGraphGraphicsRightBar[s, e, featlen], True, 
            ReleaseHold@Hold[]]}]\)], "Input",
  InitializationCell->True],

Cell["\<\
BondGraphPlot draws a bond graph using functions from the \
DiscreteMath`GraphPlot package. See the usage message for options. There is a \
lot of room for improving control over the generated graph, along with its \
documentation...\
\>", "Text",
  InitializationCell->True],

Cell[BoxData[{
    \(\(Options[BondGraphPlot] = {Method -> "\<LayeredDrawing\>", 
          BondLengthRatio \[Rule]  .5, FeatureLengthRatio \[Rule]  .175, 
          ImageSize \[Rule] Automatic};\)\), "\n", 
    \(BondGraphPlot[bg_?BondGraphQ, opts___?OptionQ] := 
      Module[{bgadjmat = BondGraphAdjacenceMatrix[bg], 
          bgjunctions = BondGraphJunctions[bg], 
          bondlenfrac = \(BondLengthRatio /. {opts}\) /. 
              Options[BondGraphPlot], 
          featlenfrac = \(FeatureLengthRatio /. {opts}\) /. 
              Options[BondGraphPlot], coords, labels}, 
        coords = 
          GraphCoordinates[bg[\([1]\)] /. {$AllowedBonds \[Rule] Rule}, 
            Method \[Rule] \((\(Method /. {opts}\) /. 
                  Options[BondGraphPlot])\)]; 
        labels = BondGraphJunctions[bg]; \[IndentingNewLine]GraphPlot[
          bg[\([1]\)] /. {$AllowedBonds \[Rule] Rule}, 
          EdgeStyleFunction \[Rule] 
            Function[
              BondGraphGraphicsBondStyleFunction[bgadjmat, bondlenfrac, 
                featlenfrac, coords[\([#1]\)], coords[\([#2]\)], #1, #2]], 
          VertexStyleFunction \[Rule] \(({Text[labels[\([#]\)], #]} &)\), 
          VertexCoordinates \[Rule] coords, 
          ImageSize \[Rule] \((\(ImageSize /. {opts}\) /. 
                Options[BondGraphPlot])\)]]\)}], "Input",
  InitializationCell->True]
}, Closed]],

Cell[CellGroupData[{

Cell["Private Definitions End", "Subsection",
  InitializationCell->True],

Cell[BoxData[
    \(\(End[];\)\)], "Input",
  InitializationCell->True]
}, Closed]],

Cell[CellGroupData[{

Cell["Package End", "Subsection",
  InitializationCell->True],

Cell[BoxData[
    \(\(EndPackage[];\)\)], "Input",
  InitializationCell->True]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Bibliography", "Section"],

Cell["\<\
[GNVNOTED] Garret N. Vanderplaats. Numerical Optimization Techniques for \
Engineering Design. With Applications. 0-944956-01-7. Copyright \[Copyright] \
2001. Vanderplaats Research & Development,
        Inc.. 1767 S. 8th Street Colorado Springs, Colorado, 80906 +1 (719) \
473-4611.\
\>", "Text"]
}, Closed]],

Cell[CellGroupData[{

Cell["Credit", "Section"],

Cell["Copyright \[Copyright] 2006 Chris Chiasson", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Licenses", "Section"],

Cell["\<\
This work is licensed to you via the MIT License or via the GPL v2.\
\>", "Text"],

Cell[CellGroupData[{

Cell["The MIT License", "Subsection"],

Cell["\<\
Permission is hereby granted, free of charge, to any person obtaining a copy \
of this software and associated documentation files (the \"Software\"), to \
deal in the Software without restriction, including without limitation the \
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or \
sell copies of the Software, and to permit persons to whom the Software is \
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in \
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR \
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, \
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE \
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER \
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, \
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE \
SOFTWARE.\
\>", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["The GPL v2", "Subsection"],

Cell["\<\
This program is free software; you can redistribute it and/or modify it under \
the terms of the GNU General Public License version 2 as published by the \
Free Software Foundation.

This program is distributed in the hope that it will be useful, but WITHOUT \
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS \
FOR A PARTICULAR PURPOSE. See the GNU General Public License for more \
details.

You should have received a copy of the GNU General Public License along with \
this program; if not, write to the Free Software Foundation, Inc., 59 Temple \
Place, Suite 330, Boston, MA 02111-1307 USA\
\>", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Text of the GPL v2", "Subsection"],

Cell["\<\
The GNU General Public License (GPL)
Version 2, June 1991

Copyright (C) 1989, 1991 Free Software Foundation, Inc.
59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.

Preamble

The licenses for most software are designed to take away your freedom to \
share and change it. By contrast, the GNU General Public License is intended \
to guarantee your freedom to share and change free software--to make sure the \
software is free for all its users. This General Public License applies to \
most of the Free Software Foundation's software and to any other program \
whose authors commit to using it. (Some other Free Software Foundation \
software is covered by the GNU Library General Public License instead.) You \
can apply it to your programs, too.

When we speak of free software, we are referring to freedom, not price. Our \
General Public Licenses are designed to make sure that you have the freedom \
to distribute copies of free software (and charge for this service if you \
wish), that you receive source code or can get it if you want it, that you \
can change the software or use pieces of it in new free programs; and that \
you know you can do these things.

To protect your rights, we need to make restrictions that forbid anyone to \
deny you these rights or to ask you to surrender the rights. These \
restrictions translate to certain responsibilities for you if you distribute \
copies of the software, or if you modify it.

For example, if you distribute copies of such a program, whether gratis or \
for a fee, you must give the recipients all the rights that you have. You \
must make sure that they, too, receive or can get the source code. And you \
must show them these terms so they know their rights.

We protect your rights with two steps: (1) copyright the software, and (2) \
offer you this license which gives you legal permission to copy, distribute \
and/or modify the software.

Also, for each author's protection and ours, we want to make certain that \
everyone understands that there is no warranty for this free software. If the \
software is modified by someone else and passed on, we want its recipients to \
know that what they have is not the original, so that any problems introduced \
by others will not reflect on the original authors' reputations.

Finally, any free program is threatened constantly by software patents. We \
wish to avoid the danger that redistributors of a free program will \
individually obtain patent licenses, in effect making the program \
proprietary. To prevent this, we have made it clear that any patent must be \
licensed for everyone's free use or not licensed at all.

The precise terms and conditions for copying, distribution and modification \
follow.

TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION

0. This License applies to any program or other work which contains a notice \
placed by the copyright holder saying it may be distributed under the terms \
of this General Public License. The \"Program\", below, refers to any such \
program or work, and a \"work based on the Program\" means either the Program \
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the Program or a portion of it, either verbatim or with modifications and/or \
translated into another language. (Hereinafter, translation is included \
without limitation in the term \"modification\".) Each licensee is addressed \
as \"you\".

Activities other than copying, distribution and modification are not covered \
by this License; they are outside its scope. The act of running the Program \
is not restricted, and the output from the Program is covered only if its \
contents constitute a work based on the Program (independent of having been \
made by running the Program). Whether that is true depends on what the \
Program does.

1. You may copy and distribute verbatim copies of the Program's source code \
as you receive it, in any medium, provided that you conspicuously and \
appropriately publish on each copy an appropriate copyright notice and \
disclaimer of warranty; keep intact all the notices that refer to this \
License and to the absence of any warranty; and give any other recipients of \
the Program a copy of this License along with the Program.

You may charge a fee for the physical act of transferring a copy, and you may \
at your option offer warranty protection in exchange for a fee.

2. You may modify your copy or copies of the Program or any portion of it, \
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modifications or work under the terms of Section 1 above, provided that you \
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    a) You must cause the modified files to carry prominent notices stating \
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    b) You must cause any work that you distribute or publish, that in whole \
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    c) If the modified program normally reads commands interactively when \
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These requirements apply to the modified work as a whole. If identifiable \
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and its terms, do not apply to those sections when you distribute them as \
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Thus, it is not the intent of this section to claim rights or contest your \
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3. You may copy and distribute the Program (or a work based on it, under \
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If any portion of this section is held invalid or unenforceable under any \
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This section is intended to make thoroughly clear what is believed to be a \
consequence of the rest of this License.

8. If the distribution and/or use of the Program is restricted in certain \
countries either by patents or by copyrighted interfaces, the original \
copyright holder who places the Program under this License may add an \
explicit geographical distribution limitation excluding those countries, so \
that distribution is permitted only in or among countries not thus excluded. \
In such case, this License incorporates the limitation as if written in the \
body of this License.

9. The Free Software Foundation may publish revised and/or new versions of \
the General Public License from time to time. Such new versions will be \
similar in spirit to the present version, but may differ in detail to address \
new problems or concerns.

Each version is given a distinguishing version number. If the Program \
specifies a version number of this License which applies to it and \"any \
later version\", you have the option of following the terms and conditions \
either of that version or of any later version published by the Free Software \
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you may choose any version ever published by the Free Software Foundation.

10. If you wish to incorporate parts of the Program into other free programs \
whose distribution conditions are different, write to the author to ask for \
permission. For software which is copyrighted by the Free Software \
Foundation, write to the Free Software Foundation; we sometimes make \
exceptions for this. Our decision will be guided by the two goals of \
preserving the free status of all derivatives of our free software and of \
promoting the sharing and reuse of software generally.

NO WARRANTY

11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR \
THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE \
STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE \
PROGRAM \"AS IS\" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, \
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND \
FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND \
PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, \
YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING \
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR \
REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, \
INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING \
OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO \
LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR \
THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER \
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE \
POSSIBILITY OF SUCH DAMAGES.

END OF TERMS AND CONDITIONS\
\>", "Text"]
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    CellMargins->{{41, Inherited}, {Inherited, Inherited}},
    FontSize->11],
  
  Cell[StyleData["Print", "SlideShow"]],
  
  Cell[StyleData["Print", "Printout"],
    CellMargins->{{39, Inherited}, {Inherited, Inherited}},
    FontSize->8]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Graphics"],
    CellMargins->{{4, Inherited}, {Inherited, Inherited}},
    CellGroupingRules->"GraphicsGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    DefaultFormatType->DefaultOutputFormatType,
    LanguageCategory->None,
    FormatType->InputForm,
    CounterIncrements->"Graphics",
    ImageMargins->{{43, Inherited}, {Inherited, 0}},
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontSize->10],
  
  Cell[StyleData["Graphics", "Presentation"],
    ImageMargins->{{62, Inherited}, {Inherited, 0}}],
  
  Cell[StyleData["Graphics", "Condensed"],
    ImageMargins->{{38, Inherited}, {Inherited, 0}},
    Magnification->0.6],
  
  Cell[StyleData["Graphics", "SlideShow"]],
  
  Cell[StyleData["Graphics", "Printout"],
    ImageMargins->{{30, Inherited}, {Inherited, 0}},
    Magnification->0.8]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["CellLabel"],
    LanguageCategory->None,
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->9,
    FontColor->RGBColor[0.269993, 0.308507, 0.6]],
  
  Cell[StyleData["CellLabel", "Presentation"],
    FontSize->12],
  
  Cell[StyleData["CellLabel", "Condensed"],
    FontSize->9],
  
  Cell[StyleData["CellLabel", "SlideShow"]],
  
  Cell[StyleData["CellLabel", "Printout"],
    FontFamily->"Courier",
    FontSize->8,
    FontSlant->"Italic",
    FontColor->GrayLevel[0]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["FrameLabel"],
    LanguageCategory->None,
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->9],
  
  Cell[StyleData["FrameLabel", "Presentation"],
    FontSize->12],
  
  Cell[StyleData["FrameLabel", "Condensed"],
    FontSize->9],
  
  Cell[StyleData["FrameLabel", "SlideShow"]],
  
  Cell[StyleData["FrameLabel", "Printout"],
    FontFamily->"Courier",
    FontSize->8,
    FontSlant->"Italic",
    FontColor->GrayLevel[0]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Inline Formatting", "Section"],
  
  Cell["\<\
These styles are for modifying individual words or letters in a cell \
exclusive of the cell tag.\
\>", "Text"],
  
  Cell[StyleData["RM"],
    StyleMenuListing->None,
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["BF"],
    StyleMenuListing->None,
    FontWeight->"Bold"],
  
  Cell[StyleData["IT"],
    StyleMenuListing->None,
    FontSlant->"Italic"],
  
  Cell[StyleData["TR"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["TI"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["TB"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Bold",
    FontSlant->"Plain"],
  
  Cell[StyleData["TBI"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Bold",
    FontSlant->"Italic"],
  
  Cell[StyleData["MR"],
    "TwoByteSyntaxCharacterAutoReplacement"->True,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["MO"],
    "TwoByteSyntaxCharacterAutoReplacement"->True,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["MB"],
    "TwoByteSyntaxCharacterAutoReplacement"->True,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Bold",
    FontSlant->"Plain"],
  
  Cell[StyleData["MBO"],
    "TwoByteSyntaxCharacterAutoReplacement"->True,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Bold",
    FontSlant->"Italic"],
  
  Cell[StyleData["SR"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["SO"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["SB"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Bold",
    FontSlant->"Plain"],
  
  Cell[StyleData["SBO"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Bold",
    FontSlant->"Italic"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["SO10"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->10,
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["SO10", "Printout"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->7,
    FontWeight->"Plain",
    FontSlant->"Italic"]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Inert"],
    StyleMenuListing->None,
    Background->RGBColor[0.870588, 0.905882, 0.972549]],
  
  Cell[StyleData["Inert", "Printout"],
    StyleMenuListing->None,
    Background->GrayLevel[1]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Formulas and Programming", "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["InlineFormula"],
    CellMargins->{{10, 4}, {0, 8}},
    CellHorizontalScrolling->True,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    LanguageCategory->"Formula",
    ScriptLevel->1,
    SingleLetterItalics->True],
  
  Cell[StyleData["InlineFormula", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5},
    FontSize->16],
  
  Cell[StyleData["InlineFormula", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1},
    FontSize->11],
  
  Cell[StyleData["InlineFormula", "SlideShow"]],
  
  Cell[StyleData["InlineFormula", "Printout"],
    CellMargins->{{2, 0}, {6, 6}},
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["DisplayFormula"],
    CellMargins->{{60, Inherited}, {Inherited, Inherited}},
    CellHorizontalScrolling->True,
    DefaultFormatType->DefaultInputFormatType,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    LanguageCategory->"Formula",
    ScriptLevel->0,
    SingleLetterItalics->True,
    UnderoverscriptBoxOptions->{LimitsPositioning->True}],
  
  Cell[StyleData["DisplayFormula", "Presentation"],
    LineSpacing->{1, 5},
    FontSize->16],
  
  Cell[StyleData["DisplayFormula", "Condensed"],
    LineSpacing->{1, 1},
    FontSize->11],
  
  Cell[StyleData["DisplayFormula", "SlideShow"]],
  
  Cell[StyleData["DisplayFormula", "Printout"],
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Program"],
    CellFrame->{{0, 0}, {0.5, 0.5}},
    CellMargins->{{60, 4}, {0, 8}},
    CellHorizontalScrolling->True,
    Hyphenation->False,
    LanguageCategory->"Formula",
    ScriptLevel->1,
    FontFamily->"Courier"],
  
  Cell[StyleData["Program", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5},
    FontSize->16],
  
  Cell[StyleData["Program", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1},
    FontSize->11],
  
  Cell[StyleData["Program", "SlideShow"]],
  
  Cell[StyleData["Program", "Printout"],
    CellMargins->{{2, 0}, {6, 6}},
    FontSize->9]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Outline Styles", "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Outline1"],
    CellMargins->{{60, 10}, {7, 7}},
    CellGroupingRules->{"SectionGrouping", 50},
    ParagraphIndent->-38,
    CounterIncrements->"Outline1",
    CounterAssignments->{{"Outline2", 0}, {"Outline3", 0}, {"Outline4", 0}},
    FontSize->18,
    FontWeight->"Bold",
    CounterBoxOptions->{
    CounterFunction:>Utilities`Notation`Private`CapitalRomanNumeral}],
  
  Cell[StyleData["Outline1", "SlideShow"]],
  
  Cell[StyleData["Outline1", "Printout"],
    CounterBoxOptions->{
    CounterFunction:>Utilities`Notation`Private`CapitalRomanNumeral}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Outline2"],
    CellMargins->{{90, 10}, {7, 7}},
    CellGroupingRules->{"SectionGrouping", 60},
    ParagraphIndent->-27,
    CounterIncrements->"Outline2",
    CounterAssignments->{{"Outline3", 0}, {"Outline4", 0}},
    FontSize->15,
    FontWeight->"Bold",
    CounterBoxOptions->{CounterFunction:>(Part[ 
        CharacterRange[ "A", "Z"], #]&)}],
  
  Cell[StyleData["Outline2", "SlideShow"]],
  
  Cell[StyleData["Outline2", "Printout"],
    CounterBoxOptions->{CounterFunction:>(Part[ 
        CharacterRange[ "A", "Z"], #]&)}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Outline3"],
    CellMargins->{{120, 10}, {7, 7}},
    CellGroupingRules->{"SectionGrouping", 70},
    ParagraphIndent->-21,
    CounterIncrements->"Outline3",
    CounterAssignments->{{"Outline4", 0}},
    FontSize->12,
    CounterBoxOptions->{CounterFunction:>Identity}],
  
  Cell[StyleData["Outline3", "SlideShow"]],
  
  Cell[StyleData["Outline3", "Printout"],
    CounterBoxOptions->{CounterFunction:>Identity}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Outline4"],
    CellMargins->{{150, 10}, {7, 7}},
    CellGroupingRules->{"SectionGrouping", 80},
    ParagraphIndent->-18,
    CounterIncrements->"Outline4",
    FontSize->10,
    CounterBoxOptions->{CounterFunction:>(Part[ 
        CharacterRange[ "a", "z"], #]&)}],
  
  Cell[StyleData["Outline4", "SlideShow"]],
  
  Cell[StyleData["Outline4", "Printout"]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Hyperlink Styles", "Section"],
  
  Cell["\<\
The cells below define styles useful for making hypertext ButtonBoxes.  The \
\"Hyperlink\" style is for links within the same Notebook, or between \
Notebooks.\
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Hyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0.269993, 0.308507, 0.6],
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2]}]&),
    Active->True,
    ButtonFrame->"None",
    ButtonNote->ButtonData}],
  
  Cell[StyleData["Hyperlink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["Hyperlink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["Hyperlink", "SlideShow"]],
  
  Cell[StyleData["Hyperlink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell["\<\
The following styles are for linking automatically to the on-line help \
system.\
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["MainBookLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0.269993, 0.308507, 0.6],
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["MainBookLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["MainBookLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["MainBookLink", "SlideShow"]],
  
  Cell[StyleData["MainBookLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["AddOnsLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0.269993, 0.308507, 0.6],
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["AddOnsLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["AddOnsLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["AddOnsLink", "SlideShow"]],
  
  Cell[StyleData["AddOnsLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["RefGuideLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0.269993, 0.308507, 0.6],
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["RefGuideLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["RefGuideLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["RefGuideLink", "SlideShow"]],
  
  Cell[StyleData["RefGuideLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["RefGuideLinkText"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0.269993, 0.308507, 0.6],
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["RefGuideLinkText", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["RefGuideLinkText", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["RefGuideLinkText", "SlideShow"]],
  
  Cell[StyleData["RefGuideLinkText", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["GettingStartedLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0.269993, 0.308507, 0.6],
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["GettingStartedLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["GettingStartedLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["GettingStartedLink", "SlideShow"]],
  
  Cell[StyleData["GettingStartedLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["DemosLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0.269993, 0.308507, 0.6],
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "Demos", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["DemosLink", "SlideShow"]],
  
  Cell[StyleData["DemosLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["TourLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0.269993, 0.308507, 0.6],
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "Tour", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["TourLink", "SlideShow"]],
  
  Cell[StyleData["TourLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["OtherInformationLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0.269993, 0.308507, 0.6],
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["OtherInformationLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["OtherInformationLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["OtherInformationLink", "SlideShow"]],
  
  Cell[StyleData["OtherInformationLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["MasterIndexLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0.269993, 0.308507, 0.6],
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "MasterIndex", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["MasterIndexLink", "SlideShow"]],
  
  Cell[StyleData["MasterIndexLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Styles for Headers and Footers", "Section"],
  
  Cell[StyleData["Header"],
    CellMargins->{{0, 0}, {4, 1}},
    DefaultNewInlineCellStyle->"None",
    LanguageCategory->"NaturalLanguage",
    StyleMenuListing->None,
    FontSize->10,
    FontSlant->"Italic"],
  
  Cell[StyleData["Footer"],
    CellMargins->{{0, 0}, {0, 4}},
    DefaultNewInlineCellStyle->"None",
    LanguageCategory->"NaturalLanguage",
    StyleMenuListing->None,
    FontSize->9,
    FontSlant->"Italic"],
  
  Cell[StyleData["PageNumber"],
    CellMargins->{{0, 0}, {4, 1}},
    StyleMenuListing->None,
    FontFamily->"Times",
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Palette Styles", "Section"],
  
  Cell["\<\
The cells below define styles that define standard ButtonFunctions, for use \
in palette buttons.\
\>", "Text"],
  
  Cell[StyleData["Paste"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, Placeholder]}]&)}],
  
  Cell[StyleData["Evaluate"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionEvaluate[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["EvaluateCell"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionMove[ 
          FrontEnd`InputNotebook[ ], All, Cell, 1], 
        FrontEnd`SelectionEvaluateCreateCell[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["CopyEvaluate"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`SelectionCreateCell[ 
          FrontEnd`InputNotebook[ ], All], 
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionEvaluate[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["CopyEvaluateCell"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`SelectionCreateCell[ 
          FrontEnd`InputNotebook[ ], All], 
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionEvaluateCreateCell[ 
          FrontEnd`InputNotebook[ ], All]}]&)}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Placeholder Styles", "Section"],
  
  Cell["\<\
The cells below define styles useful for making placeholder objects in \
palette templates.\
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Placeholder"],
    Placeholder->True,
    StyleMenuListing->None,
    FontSlant->"Italic",
    FontColor->RGBColor[0.890623, 0.864698, 0.384756],
    TagBoxOptions->{Editable->False,
    Selectable->False,
    StripWrapperBoxes->False}],
  
  Cell[StyleData["Placeholder", "Presentation"]],
  
  Cell[StyleData["Placeholder", "Condensed"]],
  
  Cell[StyleData["Placeholder", "SlideShow"]],
  
  Cell[StyleData["Placeholder", "Printout"]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["PrimaryPlaceholder"],
    StyleMenuListing->None,
    DrawHighlighted->True,
    FontSlant->"Italic",
    Background->RGBColor[0.912505, 0.891798, 0.507774],
    TagBoxOptions->{Editable->False,
    Selectable->False,
    StripWrapperBoxes->False}],
  
  Cell[StyleData["PrimaryPlaceholder", "Presentation"]],
  
  Cell[StyleData["PrimaryPlaceholder", "Condensed"]],
  
  Cell[StyleData["PrimaryPlaceholder", "SlideShow"]],
  
  Cell[StyleData["PrimaryPlaceholder", "Printout"]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["FormatType Styles", "Section"],
  
  Cell["\<\
The cells below define styles that are mixed in with the styles of most \
cells.  If a cell's FormatType matches the name of one of the styles defined \
below, then that style is applied between the cell's style and its own \
options. This is particularly true of Input and Output.\
\>", "Text"],
  
  Cell[StyleData["CellExpression"],
    PageWidth->Infinity,
    CellMargins->{{6, Inherited}, {Inherited, Inherited}},
    ShowCellLabel->False,
    ShowSpecialCharacters->False,
    AllowInlineCells->False,
    Hyphenation->False,
    AutoItalicWords->{},
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontSize->12,
    Background->GrayLevel[1]],
  
  Cell[StyleData["InputForm"],
    InputAutoReplacements->{},
    AllowInlineCells->False,
    Hyphenation->False,
    StyleMenuListing->None,
    FontFamily->"Courier"],
  
  Cell[StyleData["OutputForm"],
    PageWidth->Infinity,
    TextAlignment->Left,
    LineSpacing->{0.6, 1},
    StyleMenuListing->None,
    FontFamily->"Courier"],
  
  Cell[StyleData["StandardForm"],
    InputAutoReplacements->{
      "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", 
        ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", 
        Inherited},
    "TwoByteSyntaxCharacterAutoReplacement"->True,
    LineSpacing->{1.25, 0},
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  Cell[StyleData["TraditionalForm"],
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  Cell["\<\
The style defined below is mixed in to any cell that is in an inline cell \
within another.\
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  Cell[StyleData["InlineCell"],
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    StyleMenuListing->None],
  
  Cell[StyleData["InlineCellEditing"],
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  Cell[CellGroupData[{
  
  Cell["Automatic Styles", "Section"],
  
  Cell["\<\
The cells below define styles that are used to affect the display of certain \
types of objects in typeset expressions.  For example, \"UnmatchedBracket\" \
style defines how unmatched bracket, curly bracket, and parenthesis \
characters are displayed (typically by coloring them to make them stand out).\
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\>", "Text"],
  
  Cell[StyleData["UnmatchedBracket"],
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  Cell[StyleData["Completions"],
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  Cell[CellGroupData[{
  
  Cell["Styles from HelpBrowser", "Section"],
  
  Cell[CellGroupData[{
  
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  Cell[StyleData["MathCaption", "Presentation"],
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  Cell[StyleData["MathCaption", "SlideShow"]],
  
  Cell[StyleData["MathCaption", "Printout"],
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  Cell[CellGroupData[{
  
  Cell[StyleData["ObjectName"],
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    ShowStringCharacters->True,
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    StyleMenuListing->None,
    FontWeight->"Bold"],
  
  Cell[StyleData["ObjectName", "Presentation"],
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  Cell[StyleData["ObjectName", "SlideShow"]],
  
  Cell[StyleData["ObjectName", "Printout"],
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    CellMargins->{{39, 0}, {6, 6}},
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  Cell[CellGroupData[{
  
  Cell[StyleData["Usage"],
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    StyleMenuListing->None,
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  Cell[StyleData["Usage", "Presentation"],
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  Cell[StyleData["Usage", "SlideShow"]],
  
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  Cell[StyleData["Notes", "Presentation"],
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  Cell[StyleData["Notes", "SlideShow"]],
  
  Cell[StyleData["Notes", "Printout"],
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  Cell[CellGroupData[{
  
  Cell[StyleData["InlineOutput"],
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  Cell[StyleData["InlineOutput", "Presentation"],
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  Cell[StyleData["InlineOutput", "SlideShow"]],
  
  Cell[StyleData["InlineOutput", "Printout"],
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  Cell[CellGroupData[{
  
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  Cell[CellGroupData[{
  
  Cell[StyleData["Box"],
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  Cell[StyleData["Box", "Presentation"],
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  Cell[StyleData["Box", "SlideShow"]],
  
  Cell[StyleData["Box", "Printout"],
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  Cell[CellGroupData[{
  
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  Cell[StyleData["DoubleBox", "Presentation"],
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  Cell[StyleData["DoubleBox", "SlideShow"]],
  
  Cell[StyleData["DoubleBox", "Printout"],
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  Cell[CellGroupData[{
  
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  Cell[StyleData["1ColumnBox", "Presentation"],
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  Cell[StyleData["1ColumnBox", "SlideShow"]],
  
  Cell[StyleData["1ColumnBox", "Printout"],
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  Cell[CellGroupData[{
  
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  Cell[StyleData["2ColumnBox", "Presentation"],
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  Cell[StyleData["2ColumnBox", "SlideShow"]],
  
  Cell[StyleData["2ColumnBox", "Printout"],
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  Cell[CellGroupData[{
  
  Cell[StyleData["2ColumnEvenBox"],
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  Cell[StyleData["2ColumnEvenBox", "Presentation"],
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  Cell[StyleData["2ColumnEvenBox", "SlideShow"]],
  
  Cell[StyleData["2ColumnEvenBox", "Printout"],
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  Cell[CellGroupData[{
  
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  Cell[StyleData["2ColumnSmallBox", "Presentation"],
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  Cell[StyleData["2ColumnSmallBox", "SlideShow"]],
  
  Cell[StyleData["2ColumnSmallBox", "Printout"],
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  Cell[CellGroupData[{
  
  Cell[StyleData["3ColumnBox"],
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  Cell[StyleData["3ColumnBox", "Presentation"],
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  Cell[StyleData["3ColumnBox", "SlideShow"]],
  
  Cell[StyleData["3ColumnBox", "Printout"],
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  Cell[CellGroupData[{
  
  Cell[StyleData["3ColumnSmallBox"],
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    ColumnAlignments->{Right, Center, Left}}],
  
  Cell[StyleData["3ColumnSmallBox", "Presentation"],
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  Cell[StyleData["3ColumnSmallBox", "SlideShow"]],
  
  Cell[StyleData["3ColumnSmallBox", "Printout"],
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    FontSize->10,
    Background->GrayLevel[0.900008]]
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  Cell[CellGroupData[{
  
  Cell[StyleData["4ColumnBox"],
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    CellHorizontalScrolling->True,
    CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941],
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    LineIndent->0,
    StyleMenuListing->None,
    Background->RGBColor[0.964706, 0.929412, 0.839216],
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  Cell[StyleData["4ColumnBox", "Presentation"],
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  Cell[StyleData["4ColumnBox", "SlideShow"]],
  
  Cell[StyleData["4ColumnBox", "Printout"],
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  Cell[CellGroupData[{
  
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  Cell[StyleData["5ColumnBox", "Presentation"],
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  Cell[StyleData["5ColumnBox", "SlideShow"]],
  
  Cell[StyleData["5ColumnBox", "Printout"],
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  Cell[StyleData["6ColumnBox", "Presentation"],
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  Cell[StyleData["6ColumnBox", "SlideShow"]],
  
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  Cell[CellGroupData[{
  
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  Cell[StyleData["FramedBox", "Presentation"],
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  Cell[StyleData["FramedBox", "SlideShow"]],
  
  Cell[StyleData["FramedBox", "Printout"],
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  Cell[CellGroupData[{
  
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  Cell[StyleData["DefinitionBox", "Presentation"],
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  Cell[StyleData["DefinitionBox", "SlideShow"]],
  
  Cell[StyleData["DefinitionBox", "Printout"],
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  Cell[StyleData["DefinitionBox3Col", "Presentation"],
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  Cell[StyleData["DefinitionBox3Col", "SlideShow"]],
  
  Cell[StyleData["DefinitionBox3Col", "Printout"],
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  Cell[StyleData["DefinitionBox4Col", "Presentation"],
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  Cell[StyleData["DefinitionBox4Col", "SlideShow"]],
  
  Cell[StyleData["DefinitionBox4Col", "Printout"],
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  Cell[StyleData["DefinitionBox5Col", "SlideShow"]],
  
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  Cell[StyleData["MiddleBox", "SlideShow"]],
  
  Cell[StyleData["MiddleBox", "Printout"],
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End of Mathematica Notebook file.
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